We consider the transverse-momentum (qT ) distribution of Drell-Yan lepton pairs produced, via W and Z/γ∗ decay, in hadronic collisions. At small values of qT , we resum the logarithmically-enhanced perturbative QCD contributions up to next-to-next- to-leading logarithmic accuracy. Resummed results are consistently combined with the known O(αS2 ) fixed-order results at intermediate and large values of qT . Our calculation includes the leptonic decay of the vector boson with the corresponding spin correlations, the finite-width effects and the full dependence on the final-state lepton(s) kinematics. The computation is encoded in the numerical program DYRes, which allows the user to apply arbitrary kinematical cuts on the final-state leptons and to compute the corresponding distributions in the form of bin histograms. We present a comparison of our results with some of the available LHC data. The inclusion of the leptonic decay in the resummed cal- culation requires a theoretical discussion on the qT recoil due to the transverse momentum of the produced vector boson. We present a qT recoil procedure that is directly applica- ble to qT resummed calculations for generic production processes of high-mass systems in hadron collisions.